Let $f(x) = 3x^{2}-8x-8$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )?
Explanation: The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $3x^{2}-8x-8 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 3, b = -8, c = -8$ $ x = \dfrac{+ 8 \pm \sqrt{(-8)^{2} - 4 \cdot 3 \cdot -8}}{2 \cdot 3}$ $ x = \dfrac{8 \pm \sqrt{160}}{6}$ $ x = \dfrac{8 \pm 4\sqrt{10}}{6}$ $x =\dfrac{4 \pm 2\sqrt{10}}{3}$